Irvin is known best as a successful coach, mainly with the Montreal Canadiens, but he was inducted into the Hockey Hall of Fame as a player in 1958, largely for his exploits before coming to the NHL at the end of his career.

At age 12, Irvin was good enough to play senior hockey. A decade later, he helped the Winnipeg Monarchs win the Allan Cup, Canada's senior amateur championship, in 1915, before turning pro with Portland of the Pacific Coast Hockey Association in 1915-16. That season, Irvin scored 35 goals as a rookie.

After serving in Canada's armed forces during World War I, Irvin was reinstated as an amateur and played three seasons before returning to professional hockey with Regina of the Western Canada Hockey League in 1921.

Irvin scored 21 goals in his first of four WCHL seasons with Regina, then joined Portland of the renamed Western Hockey League for the 1925-26 season, scoring 31 goals in 30 games. The WHL folded in 1926 and the Chicago Black Hawks, an NHL expansion franchise, bought Portland, signed Irvin and named him captain.

The 34-year-old had an impressive first season, finishing second in the NHL in scoring with 36 points (18 goals, 18 assists) in 44 games, one point behind League leader Bill Cook of the New York Rangers. However, 12 games into the 1927-28 season, Irvin fractured his skull and missed the remainder of the season. He returned for 1928-29 and spent part of the season as a player-coach before retiring. Irvin finished his NHL career with 52 points (29 goals, 23 assists) in 95 games.

Irvin was hired as coach in 1930-31 and guided the Black Hawks to the Stanley Cup Final in 1931, where they lost the best-of-5 series to the Montreal Canadiens, and was let go in September 1931. Two months later, Irvin was hired by the Toronto Maple Leafs, who were winless in their first five games, and led them to the Stanley Cup title, becoming the first coach in NHL history to take over during the season to do so.

The Maple Leafs changed coaches after the 1939-40 season, replacing Irvin with Hap Day. Toronto owner Conn Smythe recommended Irvin to the Canadiens, who were coming off a 10-win season. Montreal hired Irvin, who remained with them until 1955. Under Irvin, the Canadiens won the Stanley Cup in 1944, 1946 and 1953, and advanced to the Final in five other seasons. However, the Canadiens fired him after losing the Final in 1955; he returned to Chicago for the 1955-56 before retiring with 691 regular-season wins, at the time the most by a coach in NHL history.

Irvin died on May 16, 1957 at the age of 64 and was inducted into the Hall of Fame the following year.